With increasing globalization and continuing advances in technology, a quality education in math and the sciences is critical for today's students. Therefore mastery of basic math skills is more important than ever.
The U.S. ranked 24th of 29 member nations on the 2003 Programme for International Student Assessment (PISA, 2003), demonstrating a continued lag in math and science.
The general public is concerned about this problem, and it has been prevalent in the popular press. In the 2007 National Assessment of Educational Progress, only five percent of fourth grade students and seven percent of eighth grade students attained advanced levels of mathematics.
As kids better tools are needed as interventions for today's students. Such tools may also help gifted students and students achieving at grade level, and could be important in future MLD research.
Manipulative teaching aids have been used in mathematics education for centuries. There are many in use today that are helpful in teaching the many math concepts students need to learn. The most popular manipulatives, including Cuisenaire Rods, Unifix Cubes, and Base Ten Blocks are widely accepted as standards in teaching basic mathematic concepts to young children. Over many years, a large volume of research has found that the use of manipulatives by students improves their performance. Unfortunately in many classrooms they are rarely used, due in part to problems related to convenience and effectiveness.
These tools involve many, sometimes hundreds of pieces, which are often scattered on desks, tables or floors. Much time is spent constructing the desired pieces, or finding and retrieving them. When several students are working simultaneously, classrooms can become chaotic and learning is slowed or halted. Because young children have short attention spans, these problems can cause missed opportunities for learning.
In addition, these manipulatives fall short in demonstrating many key ideas and number relationships and in bridging the gap between concrete examples and abstraction. Accordingly, it would be advantageous to provide a more convenient manipulative to fill these gaps and provide an additional, more intuitive representation of these concepts, especially the basic math facts.
In addition to manipulative, the numberline is significant features used in teaching basic math facts, as an important intermediate step between physical counters and mental abstraction. However, as yet there are no manipulatives which provide highly convenient, intuitive demonstrations using the numberline. Accordingly, it would be advantageous to provide a more intuitive manipulative teaching tool which is number-line based so that children, many of whom are visual-spatial learners, can readily understand and remember basic mathematical concepts, and begin abstraction of those concepts.
Once a student has a basic understanding of the math facts, and is ready to master rapid recall, manipulatives are less useful. When every second counts, even the most convenient manipulative is too slow. Traditional flash cards are quick, but there are traditional problems too, most notably the need for many hours of one-on-one instruction that many students never receive. Computer programs can solve that problem and others, including the need for automatic tracking of answers, instant reporting of results and trends.
Certainly these are significant advantages, and some existing computer flashcard programs are very useful. Unfortunately, many of these computer programs place more emphasis on gaming than learning. Most are low quality and do a poor job of training the user for rapid recall of the many facts. Even the more advanced computer flashcard programs, such as Math Blaster and Fastt Math, have no elements to assist students when they have difficulty with a problem, and no elements that frame the process for moving students from concrete manipulatives to virtual manipulatives in their programs.
In view of the foregoing, it would be advantageous to provide a serious practice program that calls up a helpful virtual manipulative at just the right times—a new virtual manipulative that improves understanding and retention.
It would be advantageous if this virtual manipulative could also be supplemented by an analogous real world hands-on experience that allows children to construct a personalized set of math fact strategies to be displayed by these virtual manipulative, giving students more ownership in these strategies and facts. The personalized strategies could then be stored and used in presenting the virtual manipulative reminders at critical moments when a student encounters difficulty.
It would also be advantageous if such program offered the option for computer selection of drills and practice sessions based on continuous monitoring of students' performance, along with curricula customized to the personalized strategies developed by the students using the corresponding physical manipulative.
In view of the foregoing, it would be advantageous to provide a highly convenient and effective way to translate many basic math concepts directly to the numberline, thereby advancing learning success. It would also be advantageous to provide a more intuitive way to visualize, comprehend, and memorize basic math concepts in order to bridge the gap between the concrete and the abstract for students. Yet another advantage would be to provide a computer program based on these visual impressions that builds math fact fluency stepwise for children who are memorizing addition, subtraction, multiplication and division.
While it would be desirable to provide a method and system for teaching math that provides one or more of the foregoing or other advantageous features as may be apparent to those reviewing this disclosure, the teachings disclosed herein extend to those embodiments which fall within the scope of the appended claims, regardless of whether they accomplish one or more of the above-mentioned advantages.